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Joining the nested radicals 1

What is the minimum value \(x\) can take in order for \(f(x)\): \[f(x)=\sqrt { x+\sqrt { x+\sqrt { x+\sqrt { x+\sqrt { x+\sqrt { ... } } } } } } \] to have a real number value assuming that it goes on to infinity?

If the minimum value of \(x\) can be expressed as \(-\frac{a}{b}\), find \(a+b\).\[.\]\[.\]
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